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LMFDB - The L-functions and modular forms database
Introduction
| Overview | Random |
| Universe | Knowledge |
L-functions
| Rational | All |
Modular forms
| Classical | Maass |
| Hilbert | Bianchi |
Varieties
| Elliptic curves over $\Q$ | |
| Elliptic curves over $\Q(\alpha)$ | |
| Genus 2 curves over $\Q$ | |
| Higher genus families | |
| Abelian varieties over $\F_{q}$ | |
| Belyi maps | |
Fields
| Number fields | |
| $p$-adic fields | |
Representations
| Dirichlet characters | |
| Artin representations | |
Groups
| Galois groups | |
| Sato-Tate groups | |
| Abstract groups | |
Database
A database
The LMFDB is a database of mathematical objects arising in number theory and arithmetic geometry that illustrates some of the mathematical connections predicted by the Langlands program.
Click a heading on the left to browse, or go to a random page.
Announcements
- New section on abstract groups (8/25)
- New section on Belyi maps (7/25)
- Major revision to $p$-adic fields (7/25)
- More... (and ongoing projects)
Learn more
Information is available regarding the source, reliability, and completeness of the database.
Knowls provide explanations when you need them.
Citations and acknowledgments
This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.
Contact
·
Citation
·
Acknowledgments
·
Editorial Board
·
Source
·
SageMath version 10.4
·
LMFDB Release 1.2.1